Optimal Loop Shaping and Disturbance Rejection Beyond the Nyquist Frequency using a Forward Model Disturbance Observer and Convex Optimization Based Filter Design

Loop shaping based on the disturbance observer (DOB) offers great flexibility in designing a control system's closed-loop sensitivity to external disturbances and noises. While it is well understood how to design feedback control to reject band-limited disturbances with little trade-off when a closed-loop system has a single sampling control rate, challenges arise when disturbances appear beyond the Nyquist frequency and when the speed of the feedback sensor cannot be conve-niently increased due to hardware and/or process constraints. Such is the case in hard disk drives and emerging vision-based motion control. In this paper, we propose an optimal multi rate forward model disturbance observer (MFMDOB) for intuitive, flexible, and exact rejection of band-limited disturbances beyond the Nyquist frequency. Based on the tools from Youla-Kucera parameterization, the internal model principle, multi rate analysis, and convex optimization, we translate the design objective into a set of model-based convex optimization and multi rate prediction problems, enabling optimal local-loop shaping (LLS). We provide different optimal design formulations with finite and infinite impulse response filters. Verification of the MFMDOB is conducted on a galvo scanning process model in selective laser sintering for additive manufacturing.